top button
Flag Notify
    Connect to us
      Site Registration

Site Registration

How much wine did the cask hold originally?

0 votes
369 views

8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of water is 16 : 65.
How much wine did the cask hold originally?

posted Dec 21, 2015 by Sandeep Bedi

Share this puzzle
Facebook Share Button Twitter Share Button LinkedIn Share Button

2 Answers (Check Answer ▼)


0 votes

40l.
The litres of wine drawn = 8+3*8 = 32
x being the quantity of wine the cask held originally,
16/65 = x-32/32
65x-2080 = 512
x = 39.88l
appr., x = 40 litres

answer Dec 21, 2015 by Timilehin Oki
0 votes

24 Litres!
Let the quantity of wine the cask held originally= X litres
Now, after first operation quantity of wine held by cask= X-8 litres
After second operation, the quantity of wine held by cask= (X-8) - (X-8)*8/X ...second term is the proportion of wine removed from the mixture of wine and water in second operation.
==> Held quantity = (X-8) - (8X-64)/X = (X^2-8X-8X+64)/X = (X^2-16X+64)/X
taking X^2 out of bracket term.... X^2(1-16/X+64/X^2)/X= X(1-2*8/X+(8/X)^2) = X(1-8/X)^2
Similarly, after third operation, quantity of wine held in mixture= X(1-8/X)^3
and after fourth operation, quanity held = X(1-8/X)^4
So, ratio of wine to total mixture...
(X(1-8/X)^4)/X = 16/81 =>> (1-8/X)^4 = (2/3)^4 =>> 1-8/X = 2/3 =>> (X-8)*3 = 2*X
Hence, X = 24 litres

answer Dec 22, 2015 by anonymous



Similar Puzzles
0 votes

For a tennis tournament, school ordered an equal number of yellow and white balls.
The shop delivered 30 extra white balls, making the ratio of yellow balls to white balls 1/11 : 1/9.
How many white tennis balls did the school originally order for?

+1 vote

As per the will of a late farmer, his property would have to be divided in the following way.
The eldest got half of the land and an added 2 acres. Second son received half of the remaining land plus 2 acres. Third son got half of the remaining +2 acres. But as the fourth son took half of the remaining plus 2 acres of land, there was nothing left for the fifth son.

How many acres of land did the farmer originally have?

+1 vote

You've bought your weekly egg supply at the local farm store. The first morning you have company for breakfast and use half the eggs plus one-half an egg. The next morning you use one-half of what's left plus one-half an egg. The third morning you use one-half of what's left plus one-half an egg, and on the fourth morning, you're down to one solitary egg, so you make French toast. In all this cooking, you've never had one-half an egg to carry over to the next day.
How many eggs did you buy originally?

0 votes

There are three kids and each one have some pencils. The first kid gave the second and third as many pencils as they each already had. Then, the second gave the first and third as many as they each had. Still later, the third gave the first and second as many as they each already had. Each kid now have 24 pencils.

How many pencils did each kid have originally?

+1 vote

There is a water-cask with three different water-taps. With the smallest tap, the water-cask can be filled in 20 minutes. With the middle tap, the water-cask can be filled in 12 minutes. With the largest tap, the water-cask can be filled in 5 minutes.

...